(~
c
The!
Function: Factorial, Binomial Q 0
The!
symbol
is
formed
by overstriking
the
quotation
mark ( , ) and
the
period (.).
Monadic (One-Argument) Form: Factorial !B
The
factorial
function
result
is
the
product
of
all
the
positive integers from
one
to
the
number
value
of
the
argument.
The
argument
can
be
a positive numeric scalar,
vector,
or
other
array.
The
shape
of
the
result
is
the
same as
that
of
the
argument:
p+
24-
:l.X2x3X4-
24-
!1
2
:~
4-
~'5
l.
,')
.:..
6
2
1
.1.
120
The
factorial
function
also works with decimal numbers
and
zero,
but
negative
integers are
not
allowed. When used
in
this way, factorial can be defined by use
of
the
mathematical gamma
function
- (!A)
is
equal
to
gamma (A-1):
! 3 . 1
'+
7.173~5
!O
1.
If
the
argument
is
an array,
the
function
is
extended
to
each
of
the
elements:
B
...
2
2pO
1
")
.....
:~
B
()
1.
I'Jr
.:..
3
!B
:I.
:1.
,')
..
'-
6
59
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